Logic and Computer Science: Lectures Given at the First by Scedrov A., Nerode A., Sacks G. E.

By Scedrov A., Nerode A., Sacks G. E.

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Extra resources for Logic and Computer Science: Lectures Given at the First Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held at Montecatini Terme, Italy, June 20-18, 1988

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Of course, countable compactness can also be proved easily by tableaux. We omit the set-theoretic discussion necessary to extend compactness to uncountable sets of propositions. lsupported by NSF grant DMS-89-02797 and ARO contract DAAG29-85-C-0018 BIBLIOGRAPHY Starred entries (*) contain extensive bibliographies. Part h General References M. J. Beeson(*) [1985], Foundations of Constructive Mathematics, Springer-Verlag, Berlin. An encyclopedic reference summarizing the metamathematics of constructive mathematics.

I, Studies in Proof Theory, Bibliopolis, Naples. An introduction emphasizing the ordinary mathematical structure of proof theory more than any other text currently available. A. Heyting [1956], Intuitionism: an Introduction, North-Holland, Amsterdam. The standard exposition of 1930's intuitionism. S. C. Kleene [1952], Introduction to Metamathematics, North--tIolland (1971 edition), Amsterdam. This classic text still has the best exposition of the relation between classical and intuitionist logic.

1 / N i s a n e for which g(N) suppliesa L Sucha g is called a rate of convergence function. Use as a model for computing an input--output Turing machine with an auxiliary work tape (see Hopcroft and Ullman [1979]). , in any order. A little thought shows that a Turing machine can be built which, applied to a pair of real number generators encoded on input tapes, stops if and only if those generators define distinct reals. This is because if reals are apart, that is there is an n with their difference at least l / n , then this can be detected from the sequences and their rates--of---convergence functions in a finite length of time.

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